// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_INVERSE_H
#define EIGEN_INVERSE_H

namespace Eigen {

template<typename XprType, typename StorageKind>
class InverseImpl;

namespace internal {

template<typename XprType>
struct traits<Inverse<XprType>> : traits<typename XprType::PlainObject>
{
	typedef typename XprType::PlainObject PlainObject;
	typedef traits<PlainObject> BaseTraits;
	enum
	{
		Flags = BaseTraits::Flags & RowMajorBit
	};
};

} // end namespace internal

/** \class Inverse
 *
 * \brief Expression of the inverse of another expression
 *
 * \tparam XprType the type of the expression we are taking the inverse
 *
 * This class represents an abstract expression of A.inverse()
 * and most of the time this is the only way it is used.
 *
 */
template<typename XprType>
class Inverse : public InverseImpl<XprType, typename internal::traits<XprType>::StorageKind>
{
  public:
	typedef typename XprType::StorageIndex StorageIndex;
	typedef typename XprType::Scalar Scalar;
	typedef typename internal::ref_selector<XprType>::type XprTypeNested;
	typedef typename internal::remove_all<XprTypeNested>::type XprTypeNestedCleaned;
	typedef typename internal::ref_selector<Inverse>::type Nested;
	typedef typename internal::remove_all<XprType>::type NestedExpression;

	explicit EIGEN_DEVICE_FUNC Inverse(const XprType& xpr)
		: m_xpr(xpr)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.rows(); }

	EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }

  protected:
	XprTypeNested m_xpr;
};

// Generic API dispatcher
template<typename XprType, typename StorageKind>
class InverseImpl : public internal::generic_xpr_base<Inverse<XprType>>::type
{
  public:
	typedef typename internal::generic_xpr_base<Inverse<XprType>>::type Base;
	typedef typename XprType::Scalar Scalar;

  private:
	Scalar coeff(Index row, Index col) const;
	Scalar coeff(Index i) const;
};

namespace internal {

/** \internal
 * \brief Default evaluator for Inverse expression.
 *
 * This default evaluator for Inverse expression simply evaluate the inverse into a temporary
 * by a call to internal::call_assignment_no_alias.
 * Therefore, inverse implementers only have to specialize Assignment<Dst,Inverse<...>, ...> for
 * there own nested expression.
 *
 * \sa class Inverse
 */
template<typename ArgType>
struct unary_evaluator<Inverse<ArgType>> : public evaluator<typename Inverse<ArgType>::PlainObject>
{
	typedef Inverse<ArgType> InverseType;
	typedef typename InverseType::PlainObject PlainObject;
	typedef evaluator<PlainObject> Base;

	enum
	{
		Flags = Base::Flags | EvalBeforeNestingBit
	};

	unary_evaluator(const InverseType& inv_xpr)
		: m_result(inv_xpr.rows(), inv_xpr.cols())
	{
		::new (static_cast<Base*>(this)) Base(m_result);
		internal::call_assignment_no_alias(m_result, inv_xpr);
	}

  protected:
	PlainObject m_result;
};

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_INVERSE_H
